BowleyR Documentation

Bowley's data on values of British and Irish trade, 1855-1899


In one of the first statistical textbooks, Arthur Bowley (1901) used these data to illustrate an arithmetic and graphical analysis of time-series data using the total value of British and Irish exports from 1855-1899. He presented a line graph of the time-series data, supplemented by overlaid line graphs of 3-, 5- and 10-year moving averages. His goal was to show that while the initial series showed wide variability, moving averages made the series progressively smoother.




A data frame with 45 observations on the following 2 variables.


Year, from 1855-1899


total value of British and Irish exports (millions of Pounds)


Bowley, A. L. (1901). Elements of Statistics. London: P. S. King and Son, p. 151-154.

Digitized from Bowley's graph.



# plot the data 
with(Bowley,plot(Year, Value, type='b', lwd=2, 
	ylab="Value of British and Irish Exports",
	main="Bowley's example of the method of smoothing curves"))

# find moving averages-- use center alignment (requires width=ODD)
#require(gtools, warn.conflicts=FALSE)
# simpler version using stats::filter
running <- function(x, width = 5){as.vector(stats::filter(x, rep(1 / width, width), sides = 2))}

mav3<-running(Bowley$Value, width=3)
mav5<-running(Bowley$Value, width=5)
mav9<-running(Bowley$Value, width=9)
lines(Bowley$Year, mav3, col='blue', lty=2)
lines(Bowley$Year, mav5, col='green3', lty=3)
lines(Bowley$Year, mav9, col='brown', lty=4)

# add lowess smooth
lines(lowess(Bowley), col='red', lwd=2)

if(require("ggplot2", quietly=TRUE)) {
  ggplot(aes(x=Year, y=Value), data=Bowley) +
    geom_point() +
    geom_smooth(method="loess", formula=y~x)